RE: Shutting fields down / experiences?
You're experiencing a typical problem with urban flying sites. If somebody drives down the street on a motorcycle, it gets reported as airplane noise. Parents will drive by your flying field and will decide it would look better with soccer goals all over your runway. The local police and the city parks people don't care enough to mediate complaints in a fair and thorough manner, they're more likely to ban RC flying simply to end the complaining.
Your club needs to take a long-term proactive approach for defending your rights by working for positive publicity. Put on a charity fund-raising event for a local organization and make sure you publicize it as best you can. Organize "park clean-up" days with the city parks people where the club comes out and cleans up the park next to flying field and make sure the parks people know that you're putting in extra work. When you have events or meetings out at the field, invite city councilmen or whatever other local politicians are available out to speak to the crowd. Award these local politicians with plaques and certificates for supporting RC flying so they have something to hang on their office wall.
The only way to protect your flying site is to create the notion that your flying club is a good thing. Simply put, you need to kiss a lot of butt with regard to everyone who can infuence whether or not you're allowed to continue flying.
It sounds like your club is already being pressured to pack up and move out. You probably won't have time to build up the kind of public relations campaign that might save your field. Your club, assuming it is chartered, should contact the AMA and see what kind of help is available for improving your local club profile. You guys probably also need to start shopping around for a new field.
Good luck.